Music modes are basically just a major scale in a different position. At least that's an easy way to learn them. They can be used to write songs with a different 'flavor' or 'feel' to them.
When writers use a lydian mode, the song usually has an anxious sense of excitement. When they use a dorian or aeolian mode, they are usually trying to invoke some kind of heaviness or solemnity. The feel really depends on the melody; these are just generalizations.
When we shift a major scale into different positions, we get different modes. Check out these articles to read more about where music modes come from.
In this article, we cover how to move a major scale into different modes. We'll talk about each of the seven modes and their names. Practice these by moving a major scale up by one scale degree each time.
In this lesson we'll talk about how to apply the different modes on the same key. This way instead of having the same scale in seven positions, we have seven individual sounding scales. This means you'll have to memorize the different modes' formulas.
Hope this helps! Practice hard and let me know if you have any questions!